Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…

The use of Bayesian methodology to assign grades in classroom situations is presented. Assigning a grade is viewed from a criterion, as opposed to norm, referenced perspective. Criteria include mastery of some proportion, determined by the teacher, of the subject matter covered in a course. Different levels of mastery are deemed possible and,…

Effects of blind guessing on the success of passing true-false and multiple-choice tests are investigated under a stochastic binomial model. Critical values of guessing are thresholds which signify when the effect of guessing is negligible. By checking a table of critical values assembled in this paper, one can make a decision with 95% confidence…